Quality local refinement of tetrahedral meshes based on bisection
SIAM Journal on Scientific Computing
The 4-triangles longest-side partition of triangles and linear refinement algorithms
Mathematics of Computation
Adaptive refinement of unstructured finite-element meshes
Finite Elements in Analysis and Design
A 3D refinement/derefinement algorithm for solving evolution problems
Applied Numerical Mathematics - Special issue on numerical grid generation-technologies for advanced simulations
Quality Mesh Generation in Higher Dimensions
SIAM Journal on Computing
Uniform Pointwise Convergence on Shishkin-Type Meshes for Quasi-Linear Convection-Diffusion Problems
SIAM Journal on Numerical Analysis
Mesh quality improvement and other properties in the four-triangles longest-edge partition
Computer Aided Geometric Design
The 8-tetrahedra longest-edge partition of right-type tetrahedra
Finite Elements in Analysis and Design
Original article: A local refinement algorithm for the longest-edge trisection of triangle meshes
Mathematics and Computers in Simulation
Technical note: Longest-edge algorithms for size-optimal refinement of triangulations
Computer-Aided Design
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Two asymptotic properties that arise in iterative mesh refinement of triangles are introduced and investigated. First, we provide theoretical results showing that recursive application of uniform four triangles longest-edge (4T-LE) partition to an arbitrary unstructured triangular mesh produces meshes in which the triangle pairings sharing a common longest edge asymptotically tend to cover the area of the whole mesh. As a consequence, we prove that for a triangle, the induced exterior conforming refinement zone extends on average to a few neighbor adjacent triangles. We determine the asymptotic extent of this propagating path and include results of supporting numerical experiments with uniform and adaptive mesh refinement. Similar behavior and LE propagation from a four triangle self similar (4T-SS) local subdivision alternative is analyzed and compared numerically. Hybrid 4T-LE and 4T-SS LE schemes are also considered. The results are relevant to mesh refinement in finite element and finite volume calculations as well as mesh enhancement in Computer Graphics and CAGD.